1. Field of the Invention
The present invention relates to the petroleum industry, and more particularly to development of underground reservoirs such as petroleum reservoirs or gas storage sites.
2. Description of the Prior Art
Optimization and development of a petroleum reservoir are based on the most accurate possible description of the structure, the petrophysical properties, the fluid properties, etc., of the reservoir. Specialists use a known computer tool allowing accounting for the above aspects in an approximate way which is the reservoir model. Such a model is a model of the subsoil, representative of both its structure and its behavior. Generally, this type of model is represented in a computer, it is then referred to as a numerical model. A reservoir model comprises a grid, generally three-dimensional, associated with one or more petrophysical property maps (porosity, permeability, saturation, etc.). The association assigns values of the petrophysical properties to each cell of the grid.
These well-known models, which are widely used in the petroleum industry, allow determination of many technical parameters relative to the study or the development of a reservoir such as for example, a hydrocarbon reservoir. In fact, since the reservoir model is representative of the structure of the reservoir and of the behavior thereof, engineers use it for example to determine which zones are the most likely to contain hydrocarbons, the zones in which it may be interesting/necessary to drill an injection or a production well in order to enhance hydrocarbon recovery, the type of tools to use, the properties of the fluids to be used and recovered, etc. These interpretations of reservoir models in terms of “technical development parameters” are well known. Similarly, modelling CO2 storage sites allows to monitor these sites, to detect abnormal behaviors and to predict the displacement of the injected CO2.
The purpose of a reservoir model thus is to best account for all the available information on a reservoir. A reservoir model is representative when a reservoir simulation for the model provides numerical responses that are very close to the observed historical data. What is referred to as historical data are the production data obtained from measurements in wells in response to the reservoir production (oil production, water production of one or more wells, gas/oil ratio (GOR), production water proportion (water cut)), and/or repetitive seismic data (4D seismic impedances in one or more regions, etc.). A reservoir simulation is a technique allowing simulation of fluid flows within a reservoir by software referred to as flow simulator.
Integration of all the available data is therefore essential. These data generally comprise:
Measurements, are made at certain points of the geological formation, of the modelled property, in wells for example. These data are referred to as static because they are invariable in time (on the scale of the reservoir production times) and they are directly linked with the property of interest,
“Historical data”, are production data, as for example, the fluid flow rates measured in wells, tracer concentrations and data obtained from repetitive seismic acquisition campaigns at successive times. These data are referred to as dynamic because they evolve during development and they are indirectly linked with the properties assigned to the cells of the reservoir model.
The available static data are used to define random functions for each petrophysical property, such as porosity or permeability. A representation of the spatial distribution of a petrophysical property is a realization of a random function. In general, a realization is generated, on the one hand, from a mean, a variance and a covariance function that characterizes the spatial variability of the property being studied and, on the other hand, from a single or a series of random numbers. There are many simulation techniques such as the sequential Gaussian simulation, Cholesky's method or the FFT-MA method.    Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation, Oxford Press, New York, 483 p.    Le Ravalec, M., Noetinger B., and Hu L.-Y., 2000, The FFT Moving Average (FFT-MA) Generator: An Efficient Numerical Method for Generating and Conditioning Gaussian Simulations, Mathematical Geology, 32(6), 701-723.
Techniques for integration of dynamic data (production and/or 4D seismic) in a reservoir model are known which are referred to as “history matching” techniques.
History matching modifies the parameters of a reservoir model, such as permeabilities, porosities or well skins (representing damages around the well), fault connections, etc., in order to minimize the differences between the measured historical data and the corresponding responses simulated from the model. The parameters can be linked with geographic regions, such as permeabilities or porosities around one or more wells. The difference between real data and simulated responses forms a functional referred to as the “objective function”. The history matching problem is solved by minimizing this functional.
There are several types of methods for minimizing this functional. Some require considering in the objective function all the dynamic data available over time. The integration of new data requires reconsidering all the production record during the reservoir simulations, which may involve long computing times. Furthermore, these data are sometimes acquired in real time. History matching methods have thus been developed, which allow integration of new dynamic data in the reservoir models as soon as they are acquired, while simulating only the period of time since the last acquisition. These methods are referred to as sequential. An example thereof is the Ensemble Kalman Filter (EnKF) method, which is widely used in reservoir engineering:    Evensen, G., 2007, Data assimilation: The Ensemble Kalman Filter, Berlin, Germany, Springer.
This method applies to a set of reservoir models and it provides a set of models calibrated to the dynamic data.
When it is desired to assimilate new dynamic data with the Ensemble Kalman Filter (EnKF) method, a given time in the reservoir development is considered and it is assumed that a set of models of the reservoir is known at this time. This time can correspond to the state of the reservoir before production or it can result from a previous assimilation. A reservoir simulation is then performed on each model of the time considered up to the time of acquisition of the new data. A filter is then applied in order to adjust the reservoir models and to compel them to meet the measured data.
However, this filter is applied to all of the reservoir models and it does not guarantee that the perturbed models verify the spatial variability model deduced from the static observations.